A saturation property of structures obtained by forcing with a compact family of random variables

A method for constructing Boolean-valued models of some fragments of arithmetic was developed in Krajíček (Forcing with Random Variables and Proof Complexity, London Mathematical Society Lecture Notes Series, Cambridge University Press, Cambridge, 2011 ), with the intended applications in bounded ar...

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Bibliographic Details
Published in:Archive for mathematical logic 2013-02, Vol.52 (1-2), p.19-28
Main Author: Krajicek, Jan
Format: Article
Language:English
Subjects:
Algebra
Complexity
Lectures
Mathematical Logic and Foundations
Mathematical models
Mathematics
Mathematics and Statistics
Presses
Proving
Random variables
Saturation
Series (mathematics)
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Summary:A method for constructing Boolean-valued models of some fragments of arithmetic was developed in Krajíček (Forcing with Random Variables and Proof Complexity, London Mathematical Society Lecture Notes Series, Cambridge University Press, Cambridge, 2011 ), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random variables defined on a pseudo-finite sample space. We show that under a fairly natural condition on the family [called compactness in Krajíček (Forcing with Random Variables and Proof Complexity, London Mathematical Society Lecture Notes Series, Cambridge University Press, Cambridge, 2011 )] the resulting structure has a property that is naturally interpreted as saturation for existential types. We also give an example showing that this cannot be extended to universal types.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-012-0304-9